Related papers: Statistical Topology and the Random Interstellar M…
The large-scale structure in cosmology is highly non-Gaussian at late times and small length scales, making it difficult to describe analytically. Parameter inference, data reconstruction, and data generation tasks in cosmology are greatly…
We extend field-level inference to jointly constrain the cosmological parameters $\{A,\omega_{\rm cdm},H_0\}$, in both real and redshift space. Our analyses are based on mock data generated using a perturbative forward model, with noise…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
A topological computation method, called the MGSTD method, is applied to time-series data obtained from meteorological measurement. The method gives decomposition of the dynamics into invariant sets and gradient-like transitions between…
This paper deals with the problem of detecting non-isotropic high-dimensional geometric structure in random graphs. Namely, we study a model of a random geometric graph in which vertices correspond to points generated randomly and…
Statistical mechanics describes interaction between particles of a physical system. Particle properties of the system can be modelled with a random field on a lattice and studied at different distance scales using renormalization group…
In the environmental modeling field, the exploratory analysis of responses often exhibits spatial correlation as well as some non-Gaussian attributes such as skewness and/or heavy-tailedness. Consequently, we propose a general spatial model…
Asteroseismology, i.e. the study of the internal structures of stars via their global oscillations, is a valuable tool to obtain stellar parameters such as mass, radius, surface gravity and mean density. These parameters can be obtained…
The results of numerical simulations are presented which demonstrate that liquid mirror telescope galaxy redshift surveys such as the current UBC-NASA Multi-Narrowband Survey and the future LZT Survey have the potential of discriminating…
This paper studies and critically discusses the construction of nonparametric confidence regions for density level sets. Methodologies based on both vertical variation and horizontal variation are considered. The investigations provide…
Galactic all-sky maps at very disparate frequencies, like in the radio and $\gamma$-ray regime, show similar morphological structures. This mutual information reflects the imprint of the various physical components of the interstellar…
Interstellar dust corrupts nearly every stellar observation, and accounting for it is crucial to measuring physical properties of stars. We model the dust distribution as a spatially varying latent field with a Gaussian process (GP) and…
Following the discovery of the CMB, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today.…
Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize non-signaling distributions on contextuality scenarios. This paper studies simplicial distributions on…
This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
We discuss the probability distributions of Fourier modes of cosmological density fields using the central limit theorem as it applies to weighted integrals of random fields. It is shown that if the cosmological principle holds in a certain…
The paper presents bounds for the distributions of suprema for a particular class of sub-Gaussian type random fields defined over spaces with anisotropic metrics. The results are applied to random fields related to stochastic heat equations…
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…
Large scale density modes are difficult to measure because they are sensitive to systematic observational errors in galaxy surveys, but we can study them indirectly by observing their impact on small scale perturbations. Cosmological…